ETH Zurich Workshop Presentation: A Financial Market Bifurcation Parameter

Can financial market crises be predicted? We propose a Bifurcation Parameter in this regard.


BACKGROUND: Weidlich proposes the Ising Model to describe polarization of opinions in social groups. Haken's model includes the Langevin equation of Brownian motion as a special case and references Weidlich's work as an example of more ordered states in social systems. Vaga applies Weidlich and Haken's state transition concepts to formulate the Coherent Market Hypothesis. Vaga and Nawrocki develop a novel bifurcation parameter and analyze coherent, chaotic, efficient and disordered (crisis) market states.


The Coherent Market Hypothesis provides the theoretical basis for defining a quantitative bifurcation parameter, a potential indicator crisis situations in the financial markets.


The empirical daily conditional return map from 1929 to present illustrates bullish and bearish equilibrium states (where the return map crosses zero). The slope of the conditional return map in the neighborhood of moderate returns is positive with high statistical significance.


The slope of the conditional return (CR) map governs the bifurcation process from the linear, disordered state to the more structured bull and bear states.


The bifurcation parameter is the 200 day sum of conditional returns after moderate positive returns minus the 200 day sum of conditional returns after moderate negative returns. This parameter is related to the slope of the CR map.


The Bifurcation Parameter (BP) has dropped well below -10% in crisis markets such the Crash of 1929 and Great Depression Era. In contrast, the BP didn't drop below -10% at all in the post WW II Era (1946-1975). Since the advent of computerized trading and negotiated commissions in the mid-1970s, the BP has indicated a more efficient market, though recently this indicator has fallen to levels not seen since the Great Depression Era.


In the 1929 to 1939 period, the bifurcation parameter fell well below -10% and remained there on three occasions, each of which resulted in significant market declines


In the 1999 to 2009 period there were two large declines in the Bifurcation Parameter below -10%, one coincided with rising stock prices and the other with a large decline to date.


Periods with a negative BP have a significant negative bias in the conditional return map.


Periods with a BP greater than +10% have a higher degree of bull and bear trend persistence.


Market state definitions can be based solely on the Bifurcation Parameter.


Ordered markets, including both coherent and chaotic states, outperform efficient market periods, while disordered (crisis) markets have underperformed by a large degree.


Ordered markets can be decomposed into coherent bull markets (when the prior day return is >0) or chaotic markets when the prior day return is negative.


Coherent, chaotic, efficient and crisis markets have widely varying risk and reward profiles.


The Crash of 1929 and Great Depression Era was highly volatile.


The post World War II Era enjoyed a high degree of trend persistent, coherent and chaotic markets.


Since the advent of negotiated commissions in 1975, the markets have become more efficient on average.


Returns in coherent and chaotic markets are highly statistically significant. Disordered markets (mean regressive reversals after positive returns) are also statistically significant. However due to the high volatility and relatively limited amount of data, crisis market returns are only significant to the 90% level.


The Bifurcation Parameter provides a statistically significant indicator of the coherent and chaotic market states predicted by the Coherent Market Hypothesis. However, due to the extreme volatility and limited number of crisis markets the significance of this state has only been partially established, i.e. reversals of prior day price advances.




BACKUP CHARTS



The NASDAQ Composite Index exhibited a high degree of coherence from 1971 through the year 2000. It is currently in a disordered state.



The S&P500 Index has exhibited large upside reversals in the recent mean regressive market.

Over Reaction, Disordered Market Continues

We introduce an Efficient Market state, defined as -10% < Bifurcation Parameter < +10%. This represents a market where there isn't much over reaction or under reaction to news. We also update prior coherent and chaotic market state definitions, requiring the Bifurcation Parameter to be >= +10%. Therefore the Coherent and Chaotic markets clearly represent under reaction situations and trend persistent states. We also use the prior day return, R(t) to differentiate between coherent (R(t)>=0) and chaotic (R(t)<0) states. These definitions and associated risk and returns since July 1929 are summmarized as follows:

Coherent Bull Markets
Bifurcation Parameter >= +10%
R(t) >= 0 (prior day return is positive)
RETURN 37.94%
RISK 15.05%
% TIME 24.16%

Efficient Markets
-10% < Bifurcation Parameter < +10%
RETURN 6.16%
RISK 14.85%
% TIME 45.25%

Chaotic Markets
Bifurcation Parameter > +10%
R(t) < 0 (prior day return is negative)
RETURN -13.50%
RISK 17.87%
% TIME 22.15%

Disordered Markets
Bifurcation Parameter < -10%
RETURN -17.17%
RISK 36.65%
% TIME 8.43%

International Workshop on Coping with Crises in Complex Socio-Economic Systems

ETH Zurich (Switzerland), June 8-12, 2009
Monday, June 8, 2009:
15:20 - 15:45 CAB G 51
Tonis Vaga: A Financial Market Bifurcation Parameter

Preliminary Program

Poster Presentations

Organizers

Kay Axhausen
Lars-Erik Cederman
Dirk Helbing (Coordinator)
Hans Jürgen Herrmann
Frank Schweitzer
Didier Sornette

Social systems typically feature crises, i.e. unstable and dangerous situations that are characterized by abrupt and large-scale changes. Such disruptions are very hard to predict with any precision and even harder to control. Indeed, crises often convey an impression that key decision makers have lost control and that events unfold in an unstoppable and even catastrophic way. Examples include environmental crises, the collapse of transportation systems, as well as financial and social crises such as poverty, social conflicts or wars.

These and other issues will be addressed during the meeting, which combines elements of an interdisciplinary workshop with a think tank and a summer school for young scientists. Scientists and students interested in participating in this workshop are asked to send an e-mail to Lubos Buzna (lbuzna@ethz.ch) or Amin Mazloumian (amin@gess.ethz.ch) to be included in the e-mail distribution list of this workshop.

I look forward to meeting you!
Dirk Helbing, on behalf of the organizing committee.

CURRENT MARKET: DISORDERED STATE

(click on image to expand)

During the past 12 months the Dow Industrials have had an even lower return and higher risk than the average for prior extremely disordered markets. The high volatility of extremely disordered markets includes large swings both up and down. While the stimulus and bailout programs should provide the credit necessary to eventually restore normal market structure, so far the quantitative evidence is consistent with a disordered market state.

Chaos theory and the current financial crisis

Years ago, in a letter to the editor of Physics Today (February, 1979) we noted that the “market may be considered an open system in which an adequate flow of money will effect a transition from disorder (random walk) to order (cooperative or crowd behavior).” Open systems in the physical sciences require a flow of energy to maintain an ordered state far from thermal equilibrium. For example, a laser requires energy to be pumped continuously to maintain a coherent state. In the financial markets, price stability requires a flow of money or credit. In the Great Depression, credit became scarce as the bubble in stock prices unwound after the "Roaring Twenties." The current credit crisis involves the unwinding of the housing bubble and associated derivative securities.

We define a market “attractor” as a conditional return map, i.e. the average return on the day after a prior day return, R(T-1), that falls into one of five intervals:


small price changes [-0.5% < R(T-1) < +0.5%]
moderate price increases [+0.5% < R(T-1) < +3.5%]
moderate price declines [-0.5% > R(T-1) > -3.5%]
large price increase [+3.5% < R(T-1)]
large price declines [-3.5%] > R(T-1)]

Figure 1 summarizes the average conditional return map for the Dow Jones Industrial Average over the 80 year period from 1929 to 2009. A nonlinear third order polynomial fit is shown and illustrates that the market has been trend persistent on average over this period. The slope of the return map is positive in the region of moderate returns.


Figure 1. Over the past eighty years the Dow Jones Industrial Average has been governed on average by a coherent, trend persistent dynamic.

The conditional return map in Figure 1 illustrates a bistable attractor for the market. Moderate positive returns are followed on average by further positive returns. Similarly, moderate negative returns are followed on average by further negative returns. These drifts are toward dynamic equilibrium points (where the return map crosses zero) far from the market’s long term average daily return.

Next, we identify state transitions from a mean regressive market attractor to a bistable state attractor. First we define a bifurcation parameter as the sum over 200 days of conditional returns following moderate price increases (as defined above), minus the sum over 200 days of conditional returns after moderate price declines. In a mean regressive market, where the return map has a negative slope, this metric is negative whereas in a trend persistent market it is positive. The market attractor bifurcates as this measure crosses zero.

The bifurcation parameter is plotted in Figure 2. The most significant mean regressive markets occurred in the Great Depression era of the 1930s, though there were some wild swings in this indicator. From the 1940s to about 1980, the market was primarily in a trend persistent state and fluctuations of the bifurcation parameter were primarily around a positive mean. The further the bifurcation parameter deviates from zero, the better the opportunities for short term trading: in the Great Depression era a mean reversion strategy would have offered the best chance for success; from 1940 to 1980, a trend following strategy had the odds in its favor. However, more recently with the advent of computerized trading and negotiated commissions, the market has become more efficient, with less opportunity for trading.


Figure 2. The bifurcation parameter is negative in mean reverting market states and positive in trend persistent coherent markets, reflecting the slope of the conditional return map for moderate returns.


Figure 3 illustrates the market return map or attractor for market periods between 1929 and 2009 when the bifurcation parameter is negative. In this situation, moderate positive returns are followed on average by negative returns on the following day; moderate negative returns are followed by positive returns on average.


Figure 3. The market is mean regressive when the slope of the conditional return map and the bifurcation parameter are negative.

Recently the bifurcation parameter has dropped deeply into negative territory. This is an unusual development since this indicator hasn’t fallen this far since the Great Depression era. A short term trading strategy designed to profit from the market’s regression to the mean after moderate returns is appropriate in this market state. A strategy of avoiding equity positions entirely when the bifurcation parameter drops below -10% is illustrated in Figure 4. This straategy would have outperformed a buy and hold both in the Crash of 1929 and also successfully avoided much of the recent market meltdown. However, there is no assurance as to how it will work in the future particularly as it is based on a lagging indicator of market dynamics.


Figure 4. Avoiding mean reverting markets (negative bifurcation parameter) has shown profitable back testing results, but may not work in future markets.

kaoseteooria ja majanduskriis

Leo Võhandu, TTÜ emeriitprofessor



For complete article, click here

Kaos tähendab igapäevakeeles täielikku segadust ja korralagedust. Füüsikas tähendab see mingi süsteemi osiste vastastikust mittelineaarset mõjutamist koos kõigi või peaaegu kõigi süsteemsete liikumiste ebastabiilsusega. Keerulisevõitu väljend on, aga asja olemuse seletab ilusasti ära.

Et füüsikud ja mehaanikud kaoses päris hästi orienteeruvad, siis heietab nii mõnigi lootust, et ehk aitab kaoseteooria meil kriisiolukorrast pääseda. Kiiret lahendust see teooria muidugi pakkuda ei saa, aga üht-teist kasulikku majanduse ja valuutaturgude jaoks võib sealt leida küll.

Kõigepealt märgime, et eesti keeles on ilmunud kahe akadeemiku sulest kaks head ja loetavat raamatut kaoseteooria radadelt. Esimene neist pärineb Tartu Ülikooli mehaanika emeriitprofessori Ülo Lepiku sulest – «Kaos ja kord» (1997). Teise ja hoopis kopsakama raamatu kirjutasid akadeemikud Ülo Lepik ja Jüri Engelbrecht paar aastat hiljem. Selle pealkiri «Kaoseraamat» on küll lühike, aga sisu on see-eest õige huvitav.

...

Kummalisel kombel on just kaks Eestiga tugevalt seotud meest tõestanud, et kaoseteooriast on rikkaks saamise mõttes õige palju kasu.

Veidi vanem neist kahest kannab nime Tõnis Vaga. Usutavasti on ta praegu maailmas kõige tsiteeritum eestlasest majandusteadlane. See on mees, kes 1994. aastal avaldas põhjapaneva ingliskeelse raamatu: Tonis Vaga «Profiting from Chaos» («Kaosest tulu teenimine»). Mul õnnestus see raamat poolkogemata 1995. aastal ühest Tallinna raamatupoest leida ja osta. Alguses arvasin, et on tegu mõne lõunaameeriklasega, kuid järsku taipasin, et selle nime taga võib olla hoopis eestlane Tõnis. Asi sai kohe klaariks, kui vaatasin raamatu pühenduste lehekülge. Üks pühendustest oli tütrele nimega Maie. Nii et oligi eestlane. Pärastine internetikontroll tõestas kah, et tegu on praegu 60-aastase üpris tragi USA eesti kogukonna liikmega.

Vaga on hariduselt füüsik, kuid 1979. aastal avaldas ta ülimalt olulise artikli aktsiaturu hindade kõikumisest ja hiljem ka nn koherentsete turgude teooria, mis mõlemad äratasid majandusteadlaste hulgas suurt tähelepanu. Nii ta asuski oma ideid majanduses realiseerima suurfirma Booz Allen Hamilton vanempartnerina. Muide, Vaga raamatut ei leia te ühestki Eesti raamatukogust, küll aga on see vabalt kõigile kättesaadav Google’i elektronraamatute hulgas.

Teine Eestist pärit mees, kelle kirjutatud raamatud valuutaturgudel kauplemisest USAs õige menukad on, on Alexander Elder. Vagast aasta nooremana sündis ta küll Leningradis, kuid elas Eestis ja õppis Tartus meditsiini. Ta asus tööle kalalaeva arstina. Aafrika ranna lähedal kala püüdes hüppas ta laevalt ära läände ning sai USAs poliitilise varjupaiga. Elder töötas psühhiaatrina New Yorgis ja õpetas muide ka Columbia Ülikoolis.

Psühhiaatrina pakkus valuutaturg talle omamoodi väljakutset ning nüüdseks on ta kirjutanud paraja paki väga menukaid raamatuid valuutaturgudel kauplemisest. Neid raamatuid on tõlgitud 12 keelde. Tartu Ülikooli raamatukogus on Elderi raamatutest olemas viis, Tallinna raamatukogudes mitte ühtegi...

Nonlinear and Chaotic Dynamics and its Application to Historical Financial Markets

Hartmut Kiehling*

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Abstract: For roughly 15 years, economic research has been involved with chaotic systems. During these years chaos theory took a firm place in science, although the enthusiasm of the first decade was followed by a more subdued kind of consideration. This might be the time to sum up some of the results and to develop some ideas concerning possible applications of chaos theory to economic history (and its theory). Since a good portion of the chaos research that has been done until now deals with financial markets, we will consider that section of economics.

* Address all communications to Hartmut Kiehling, Heerstraße 9, D-81247 München,
Tel. +49-(0)89-8116379, Fax. +49-(0)89-8110189, e-mail: 101520.2007@compu-serve.com, 0898110189@t-online.de.

T. Vaga published his Coherent Market Hypothesis as a nonlinear statistical model. He distinguishes four market phases: random walk, transition, chaotic markets, and coherent markets. Each one is characterized by different kinds of attitudes and the mutual influence of investors. The model follows the psychological theory of social imitation, but is formulated mathematically. 15